Fluctuating crosstalk, deterministic noise, and GA scalability

This paper extends previous work showing how fluctuating crosstalk in a deterministic fitness function introduces noise into genetic algorithms. In that work, we modeled fluctuating crosstalk or nonlinear interactions among building blocks via higher-order Walsh coefficients. The fluctuating crosstalk behaved like exogenous noise and could be handled by increasing the population size and run duration. This behavior held until the strength of the crosstalk far exceeded the underlying fitness variance by a certain factor empirically observed. This paper extends that work by considering fluctuating crosstalk effects on genetic algorithm scalability using smaller-ordered Walsh coefficients on two extremes of building block scaling: uniformly-scaled and exponentially-scaled building blocks. Uniformly-scaled building blocks prove to be more sensitive to fluctuating crosstalk than do exponentially-scaled building blocks in terms of function evaluations and run duration but less sensitive to population sizing for large building-block interactions. Our results also have implications for the relative performance of building-block-wise mutation over crossover.